Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture PDF Download

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Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

Author: Rafael von Känel
Publisher: American Mathematical Society
ISBN: 1470464160
Category : Mathematics
Languages : en
Pages : 154

Book Description
View the abstract.

Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

Author: Rafael von Känel
Publisher: American Mathematical Society
ISBN: 1470464160
Category : Mathematics
Languages : en
Pages : 154

Book Description
View the abstract.

Arithmetic Geometry, Number Theory, and Computation

Author: Jennifer S. Balakrishnan
Publisher: Springer Nature
ISBN: 3030809145
Category : Mathematics
Languages : en
Pages : 587

Book Description
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.

Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1009050036
Category : Mathematics
Languages : en
Pages : 242

Book Description
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.

Number Theory

Author: Kağan Kurşungöz
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110761114
Category : Mathematics
Languages : en
Pages : 112

Book Description
Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory. Original research is presented that discusses modern techniques and survey papers from selected academic scholars.

Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties

Author: Paola Comparin
Publisher: American Mathematical Soc.
ISBN: 1470453274
Category : Education
Languages : en
Pages : 282

Book Description
Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018. The papers cover recent developments on the theory of algebraic varieties—in particular, of their automorphism groups and moduli spaces. They will be of interest to anyone working in the area, as well as young mathematicians and students interested in complex and algebraic geometry.

Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture PDF Download

Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

Solving $S$-Unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

Arithmetic Geometry, Number Theory, and Computation

Effective Results and Methods for Diophantine Equations over Finitely Generated Domains

Number Theory

Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties

Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits

On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type

Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds

Analyticity Results in Bernoulli Percolation

Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity